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A132353
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a(n)=3a(n-1)-a(n-3)+3a(n-4).
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2
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1, 2, 6, 20, 61, 183, 547, 1640, 4920, 14762, 44287, 132861, 398581, 1195742, 3587226, 10761680, 32285041, 96855123, 290565367, 871696100, 2615088300, 7845264902, 23535794707, 70607384121, 211822152361, 635466457082
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A132868(n)-a(n)=A128834(n) (discovered in 1995).
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FORMULA
| Also a(n)-3^(n+1)=hexaperiodic 1, -1, -3, -1, 1, 3; cf. A132951.
O.g.f.: -(1-x+3x^3)/[(3x-1)(1+x)(x^2-x+1)]. a(n)=-(-1)^n/12+3^(n+1)/4+A057079(n+2)/ 3. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 04 2008
a(n)=(1/6)*{1/2-(1/2)*I*sqrt(3)}^n+(3/4)*3^n-(1/12)*(-1)^n+(1/6)*{1/2+(1/2)*I*sqrt(3)}^n-(1/ 6 )*I*{1/2-(1/2)*I*sqrt(3)}^n*sqrt(3)+(1/6)*I*{1/2+(1/2)*I*sqrt(3)}^n*sqrt(3), with n>=0 and I=sqrt(-1) - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 09 2008
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CROSSREFS
| Cf. A129339.
Sequence in context: A134293 A136883 A057766 * A052958 A177792 A193235
Adjacent sequences: A132350 A132351 A132352 * A132354 A132355 A132356
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KEYWORD
| nonn
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Nov 24 2007
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 04 2008
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